Magnetism And Matter - Electromagnetism PYQ

The plane of a dip circle is set in the geographic meridian and the apparent dip is \(\delta_1\). It is then set in a vertical plane perpendicular to the geographic meridian. The apparent dip angle is \(\delta_2\). The declination \(\theta\) at the place is

A paramagnetic sample showing a net magnetisation of \(0.8 \mathrm{~A} \mathrm{~m}^{-1}\), when placed in an external magnetic field of strength \(0.8 \mathrm{~T}\), at a temperature \(5 \mathrm{~K}\). If the temperature is raised to \(20 \mathrm{~K}\), then the magnetisation becomes

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at \(30^{\circ}\) with the horizontal. The horizontal component of the earth's magnetic field at the place is 0.3 G . Then the magnitude of the earth's magnetic field at the location is

A steel wire of length \(l\) and magnetic moment \(M\) is bent into a semicircular arc of radius \(R\). The new magnetic moment is

A compass needle oscillates 20 times per minute at a place where the dip is \(45^{\circ}\) and the magnetic field is \(B_1\). The same needle oscillates 30 times per minute at a place where the dip is \(30^{\circ}\) and magnetic field is \(B_2\). Then, \(B_1: B_2\) is

Two short magnets of equal dipole moments \(M\) are fastened perpendicularly at their centres. The magnitude of the magnetic field at a distance \(d\) from the centre on the bisector of the right angle is (\(\mu_0=\) Permeability of free space)

A short bar magnet is placed in a uniform magnetic field of 2 T such that the axis of the magnet makes an angle of $45^{\circ}$ with the direction of the magnetic field. If the torque acting on the magnet is $0.36 \sqrt{2} \mathrm{~N}-\mathrm{m}$, then the moment of the magnet is

A short bar magnet of magnetic moment $10^4 \mathrm{JT}^{-1}$ is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from the direction parallel to a horizontal magnetic field of $4 \times 10^{-5} \mathrm{~T}$ to a direction $60^{\circ}$ to the direction of the field is

A short bar magnet has a magnetic moment of $0.48 \mathrm{JT}^{-1}$. The magnitude of magnetic field at a point at 10 cm distance from the centre of the magnet on its axis is

The work done in rotating a bar magnet which is initially in the direction of a uniform magnetic field through $45^{\circ}$ is $W$. The additional work to be done to rotate the magnet further through $15^{\circ}$ is

A sample of paramagnetic salt contains $2 \times 10^{24}$ atomic dipoles each of dipole moment $15 \times 10^{-23} \mathrm{JT}^{-1}$. The sample is placed under homogeneous magnetic field of 0.6 T and cooled to a temperature 4.2 K . The degree of magnetic saturation achived is $20 \%$. Then total dipole moment of the sample for a magnetic field of 0.9 T and a temperature of 2.8 K is

A sample of a ferromagnetic iron in the shape of a cube of side $1.0 \mu \mathrm{~m}$ contains $8.7 \times 10^{28}$ atoms per cubic metre and the magnetic dipole moment of each iron atom is $93 \times 10^{-24} \mathrm{Am}^2$. Then, the maximum possible magnetic dipole moment (in $\mathrm{Am}^2$ ) of the sample is nearly